An upper diameter bound for compact Ricci solitons with application to the Hitchin–Thorpe inequality. II

Abstract

In this addendum to the author’s paper [H. Tadano, J. Math. Phys. 58, 023503 (2017)], by using an upper diameter bound for compact shrinking Ricci solitons by Wu [preprint arXiv:1706.07897 (2017)], we shall give a new sufficient condition for compact four-dimensional shrinking Ricci solitons to satisfy the Hitchin–Thorpe inequality. Our new condition sharpens the validity of the Hitchin–Thorpe inequality given by Tadano [J. Math. Phys. 58, 023503 (2017)].